We see that Eq. (REF ) involves cyclic constraints from the \(s\) -channel \(\langle  {\bf a}_2 , i_s , i_s+2 \rangle _{i_s \ge 2}\) , similarly from the \(u\) -channel \( \langle  {\bf a}_2 , (i_u+1)^{(2)} , i_u^{(2)} \rangle _{i_u \ge 4}\) , as well as a mixed constraint \( \langle  {\bf a}_2 , 4_u^{(2)} , 2_s \rangle \)  that involves low-spin partial waves. This phenomenon observed in Ref. [1]} continues to hold for higher \(k\)  as well. It allows us to easily identify the set of conditions that carve out the region of allowed couplings analytically rather straightforwardly by inspecting the low-spin boundaries. Of course, in practice we only look for possible boundaries up to some finite spin \(J_{{\rm max}}\)  and assume that the observed pattern continues all the way to \(J_{{\rm max}} = \infty \) .
